TSTP Solution File: SWV331-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV331-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:14 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 39
% Syntax : Number of formulae : 61 ( 14 unt; 18 typ; 0 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 384 ( 186 ~; 173 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 97 ( 87 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_in_type,type,
c_in: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_Message_OkeysFor_type,type,
c_Message_OkeysFor: $i > $i ).
tff(c_Message_Oparts_type,type,
c_Message_Oparts: $i > $i ).
tff(c_Event_Oknows_type,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(v_evs3_type,type,
v_evs3: $i ).
tff(c_Message_Oagent_OSpy_type,type,
c_Message_Oagent_OSpy: $i ).
tff(v_K_type,type,
v_K: $i ).
tff(c_Message_OsymKeys_type,type,
c_Message_OsymKeys: $i ).
tff(tc_List_Olist_type,type,
tc_List_Olist: $i > $i ).
tff(tc_Event_Oevent_type,type,
tc_Event_Oevent: $i ).
tff(c_Yahalom_Oyahalom_type,type,
c_Yahalom_Oyahalom: $i ).
tff(tc_Message_Omsg_type,type,
tc_Message_Omsg: $i ).
tff(c_Event_Oused_type,type,
c_Event_Oused: $i > $i ).
tff(c_Message_Omsg_OKey_type,type,
c_Message_Omsg_OKey: $i > $i ).
tff(c_Message_Omsg_OCrypt_type,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce_type,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(v_NB_type,type,
v_NB: $i ).
tff(1,plain,
^ [V_K: $i,V_evs: $i] :
refl(
( ( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
<=> ( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
<=> ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
<=> ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [V_K: $i,V_evs: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ) )),
rewrite(
( ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) ) )),
rewrite(
( ( ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
( ( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V_K: $i,V_evs: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) )
<=> ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [V_K: $i,V_evs: $i] :
( ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Yahalom_Onew__keys__not__used_0) ).
tff(7,plain,
! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( c_in(v_K,c_Message_OsymKeys,tc_nat)
<=> c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
c_in(v_K,c_Message_OsymKeys,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tff(13,plain,
c_in(v_K,c_Message_OsymKeys,tc_nat),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
<=> ~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
tff(16,plain,
~ c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
<=> c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(19,plain,
c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent)),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ( ~ ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat) )
<=> ( ~ ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_K: $i,V_evs: $i] :
( c_in(c_Message_Omsg_OKey(V_K),c_Event_Oused(V_evs),tc_Message_Omsg)
| ~ c_in(V_evs,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(V_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,V_evs))),tc_nat) )
| c_in(c_Message_Omsg_OKey(v_K),c_Event_Oused(v_evs3),tc_Message_Omsg)
| ~ c_in(v_evs3,c_Yahalom_Oyahalom,tc_List_Olist(tc_Event_Oevent))
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat),
inference(unit_resolution,[status(thm)],[22,19,16,13,10]) ).
tff(24,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
refl(
( ( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [V_H: $i,V_X: $i,V_K: $i] :
rewrite(
( ( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(V_H),tc_nat) )
<=> ( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V_H: $i,V_X: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(V_H),tc_nat) )
<=> ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V_H: $i,V_X: $i,V_K: $i] :
( ~ c_in(V_K,c_Message_OsymKeys,tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| c_in(V_K,c_Message_OkeysFor(V_H),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_OCrypt__imp__keysFor_0) ).
tff(30,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
<=> c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
tff(36,plain,
c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) )
<=> ( ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) )
<=> ( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg)
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V_H: $i,V_X: $i,V_K: $i] :
( c_in(V_K,c_Message_OkeysFor(V_H),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(V_K,V_X),V_H,tc_Message_Omsg)
| ~ c_in(V_K,c_Message_OsymKeys,tc_nat) )
| ~ c_in(v_K,c_Message_OsymKeys,tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3))),tc_nat)
| ~ c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs3)),tc_Message_Omsg) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
$false,
inference(unit_resolution,[status(thm)],[42,13,36,33,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV331-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:31:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.38 % SZS status Unsatisfiable
% 0.13/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------